A vertical radio mast 24 m tall stands on flat ground. At a time when the sun is \(30^\circ\) above the horizon, how long is the shadow of the mast?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(24\sqrt{3}\) m
The sun's ray from the top of the mast to the tip of the shadow meets the ground at the sun's angle of elevation, \(30^\circ\). The mast is the side opposite this angle and the shadow is the side next to it, so they are linked by the tangent.
\(\tan 30^\circ=\displaystyle\frac{24}{\text{shadow}}\)
Shadow \(=\displaystyle\frac{24}{\tan 30^\circ}=24\times\sqrt{3}=24\sqrt{3}\) m
